Question

There are 72 boys and 90 girls in a class. For Maths competition teacher would like to make teams for boys and girls separately but number of students should remain same in each team. What is the greatest number of students that can be in one of such teams options 6 12 18 24​

Answer 1

Answer:

There are 72 boys and 90 girls in a class. For Maths competition teacher would like to make teams for boys and girls separately but number of students should remain same in each team. What is the greatest number of students that can be in one of such teams options 6 12 18 24

Answer 2

Answer:

Given:

72 boys

90 girls

objective: to arrange in rows with equal number (n) of only boys or girls.

To find the maximum number (n) of boys or girls in each row, we need to find the GCF (Greatest Common Factor) of the numbers 72 and 90, such that n divides both numbers evenly without a remainder.

We will use two methods to find the GCF of two numbers.

Method 1

Factorize each number to powers of prime and locate the common factors.

72+=+2%5E3%2A3%5E2

90+=+2%2A3%5E2%2A5

So the GCF is 2%2A3%5E2=18

Method 2 (Euclid division)

step 1: divide the larger number by the small number, reject the quotient

step 2: if the remainder is 0, the smaller number is the GCF

if the remainder is greater than zero, replace the larger number by the remainder (which becomes the smaller number), repeat step 1.

We will use the folowing symbols

L=larger number

S=smaller number

R=remainder

L S R

90 72 18 90%2F72=1 with remainder 18

72 18 0 72%2F18=4 with remainder 0

Therefore 18 is the GCF

Answer: the students can be arranged in rows of 18, that is 4 rows of boys and 5 rows of girls.